It said demand for experienced production staff is “far outstripping supply”.
The sector has been valued at £567 million and supports thousands of jobs.
Recent movies to have been shot in Scotland include the new Indiana Jones and Batman films, while TV productions include the Scottish-set dramas Crime, Guilt, Shetland, The Control Room and Vigil.
Screen Scotland is now commissioning research to map the current further and higher education provision for film and TV in Scotland.
It said that “in order to understand the need, and the size and scale of anything resembling a 'film school’, there is a need for rigorous, qualitative and quantitative research into what Scotland already has in place”.
A contract document reads: “Denmark has one; London has several. But Scotland has no dedicated institution called a ‘film school’.
"It does, however, have a healthy range of training and higher and further education institutions providing film and media related courses, many of which are highly regarded.
"Added to this are a range of non-formal education and training opportunities, largely delivered by the members of the Screen Training Alliance, and apprenticeships in a narrow range of areas largely provided by the BBC.
“Is the lack of a dedicated film school in Scotland a problem that requires a remedy?”
Screen Scotland said there are a number of challenges and opportunities facing the country, including “unprecedented demand, far outstripping supply, for locally-based, experienced craft and technical production personnel to work on large scale, high-end TV and film projects”.
It said there is a “need to develop creative, entrepreneurial producers capable of developing and raising finance for high-end TV and film projects”, warning: “Without such a cohort of producers, Scotland will fall behind globally in a world now dominated by streaming platforms and will have little to no ability to sustain and grow production companies of scale.
"Nor will global audiences be able to enjoy films, documentaries and TV series of scale that have been originated in Scotland, representing a missed opportunity to sustain its international cultural reach.”
The research contract has a value of between £8,000 and £10,000, with a final report set to be delivered by December.
Mr Robertson said: “The Scottish screen sector is of massive cultural value and has significant economic impact, as demonstrated by Screen Scotland’s June 2022 report, Economic Value of the Screen Sector in Scotland.
“The Scottish Government is focused on building the skills, talent, a support system and infrastructure to capitalise on unprecedented interest in production in Scotland and further develop a sustainable creative economy.”
A Screen Scotland spokeswoman said: “In line with our role as the development agency for Scotland’s screen sector, this invitation to tender is part of our long-term planning, exploring potential development options for the future.
"We look forward to working with the successful bidder, and to seeing the outcomes and recommendations.”